I generated factor scores using approach in Example 11.7, using NDATASETS=50. I also saved plausible values along with mean, median, etc. in separate file (Thanks for pointing me to that example, Linda...).

I then analyzed latent structural model based on those factor scores, using Example 13.13 method. (All variables are continuous.).

There was a considerable difference between ML and MLR estimators in terms of test of fit, RMSEA, CFI/TLI, and SRMR:

Also (is probably a na´ve question), is there a way to incorporate the Bayes-generated plausible factor score values and distribution information (as per the Example 11.7 SAVEDATA: file=ex11.7plaus.dat ...) into an analysis testing relationships among those latent variables using a Bayes estimator?

Or is my use of the imputation approach (as described in previous post) essentially the same thing, so I have basically already done that?

So, to be sure I understand - the factor scores generated in the imputed data sets in the original measurement model, using Bayes estimator, reflect the variability in the values, so that the analysis using the imputation data sets incorporates / reflects the error variance for those latent variable values estimated in the original measurement model.